Year: 2010
Type: dissertation
Abstract: We study the dynamics of homoclinic classes on three dimensionalmanifolds under the robust absence of dominated splittings. We prove that, C1-generically, if such a homoclinic class contains a volume-expanding periodic point, then it contains a hyperbolic periodic point whose index(dimension of the unstable manifold) is equal to two. We also furnish anexample which shows that a similar result is not always true in higherdimensions.
DOI: 10.15083/00004024
Author: Katsutoshi Shinohara
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W96359799